Applied Mechaics ad Materials Olie: 202--2 ISSN: 662-7482 Vols 27-29 pp 2649-2653 doi:04028/wwwscietificet/amm27-292649 202 Tras Tech Publicatios Switzerlad The study of fault-diagosis method of reciprocatig compressor based o fuzzy fault tree theory Jia-Chu Gog a PENG-Fei Tia 2b 2 PaZhiHua Uiversity chia 67000 a cgog0@63com b tiapegfeisust@qqcom Keywords: reciprocatig compressor fuzzy set theory fault tree diagosis Abstract Sice workig coditio of reciprocatig compressor is awfully bad ad it has bigger risk i operatio ad higher fault rate it is of importace to study reciprocatig compressor fault Fault tree has bee established i this paper by aalyzig factors leadig reciprocatig compressor fault based o the method of fault tree 2 miimum cut sets leadig to reciprocatig compressor fault ca be gotte through qualitative aalyses o this fault tree the happeig probability of the top evet ca be calculated ad the importace of the basic evet s ca be aalyzed through quatitative aalysis The expert iquiry method combied with fuzzy sets theory is adopted to assess the happeig probability of the basic evets ad top evets Reciprocatig compressor is extesively used i may petroleum ad chemical eterprises for high compressio ratio of sigle stage ad high work efficiecy Oce the machies are abormal ad fault it will affect the ormal productio brig huge ecoomic loss Developmet of reciprocatig compressor fault diagosis fault elimiatio ca be ivisible the ormal operatio of the machie ca be esured ecoomic beefit be improved Applicatio of fuzzy fault tree theory ca effectively diagose reciprocatig compressor failure probability ad quickly idetify the predisposig factors causig failure Costructio of fault tree Fault Tree Aalysis called FTA method for short is a kid of aalysis method that refies system fault formatio reaso from geeral to part accordig to the dedrimers So it is aalysis tool for the complicated dyamic system desig factory test or field foud that the failure forms of reliability FTA method is desiged to ascertai the basic fault determiig the cause of the malfuctio the [2] probability of occurrece ad impact Costructio of fault tree i fault tree aalysis is the most basic the most crucial lik also the premise coditio of fault tree aalysis For the same system a differet fault trees will be built by differet people accordig to differet eeds ad differet trai of thought But i the process of establishmet of fault tree the fault effect failure mode ad failure mechaism aalysis must be aalysised Oce the top evet is idetified the fault tree will be layer-by-layer built For reciprocatig compressor the faults of the air valve pressure packig rig fault Pisto rig fault pisto ad pisto rod cylider fault cylider fault oil wiper fault are the mai failure evets Because each elemet i the system are relatively idepedet each compoet is treated as fault subsystem idetified as itermediate evet The fault tree ca be layer-by-layer built The evet code is as follows reciprocatig compressor failure as the top evet is expressed i T Valve fault i Epressure packig rig fault i E2; fault of pisto rig i e3; pisto ad pisto rod cylider fault i E4; Cylider fault i E5; oil wiper fault i E6; valve failure i E7; sprig failure i E8 valve plate surface debris 2 the valve fracture sprig 3 ier surface crack 4 improper selectio of sprig 5 sprig 6 pisto rod ad a packig rig frictio ad wear 7 filler rod ad the pisto rod seal failure 8 packig box temperature icreased 9 pisto rig gap too small 0 pisto rig [] [ 35] All rights reserved No part of cotets of this paper may be reproduced or trasmitted i ay form or by ay meas without the writte permissio of Tras Tech Publicatios wwwttpet (ID: 302033675 Pesylvaia State Uiversity Uiversity Park USA-05/03/69:44:27
2650 Advaced Materials ad Process Techology tesio too large pisto ad pisto rod of the mechaical properties ad smoothess does ot meet the requiremets 2 the pisto rod ad the pisto are ot firmly coected 3 pisto rod positioig termial ad the cetral lie of the pisto verticality does ot meet the requiremets 4 coolig water system i short supply 5 lubricatio system oil supply shortage 6 suctio valve cavity leakage 7 Exhaust valve ammed or broke 8 oil wiper wear 9 scrapig the oil rig icorrectly istalled 20 pisto rod wor or scratched 2 rig side clearace abormalities Fig The effect fault tree diagram of reciprocatig compressor I the above fault tree model there is oly a sigle logical" or" door It is said that the output evet will occur whe oe or more of the iput evet occurs Therefore oce there is oe evet of the iput logic" or" door several itermediate evets its upper level failure evet will happe reciprocatig compressor will be ieffective [ 6] Fault tree aalysis of reciprocatig compressor ( Structure fuctio of fault tree Fault tree structure fuctio is to use simple mathematical expressios i the form of fault tree i order to simplify the fault tree operate by usig mathematical method diagosis ad deal with the fault by computer Figure shows the reciprocatig compressor fault tree by the OR door evet expressio its ( Y xi max( x x2 x2 structure fuctio expressed as i 2 2 Y x 2 i I xi Y i the formula express i i( (2 I the formula: x ( i 22 as the top evet status i as the bottom evet status decided x by i 2 completely(total of 2 states O the represetatio whe the system has a bottom evet occurs the top evet occurs As ca be see the reciprocatig compressor fault tree without too much logic algebra rules for simplificatio it ca be behid the fuzzy fault tree aalysis The qualitative aalysis ad the quatitative aalysis Qualitative aalysis of fault tree is calculated all miimal cut sets the mai methods of miimum cut set are determiat method structural method ad Boolea algebraic simplificatio methodi this paper the fault tree is trasformed ito a equivalet Boolea algebra equatio usig Boolea algebraic simplificatio method Reciprocatig Compressors is o the blik (T the formula is as T follows(3: 2 i i ( (3
Applied Mechaics ad Materials Vols 27-29 265 K K2 K supposed as all the miimal cut sets of fault tree of kow fault tree =2If the Q ( kow basic probability is i P i i 22 the fault tree ( T top evet occurrece probability calculatio formula is as follows: T P K K Q i i K i 2 _ Ki K _ KiK Kk ( KK2 K i k ik (4 Because the probability of bottom evet is very small the type (4 depeds oly o the first The structure importat degree aalysis is the importace degree of aalysis of the basic evets Cosiderig the basic evet probability chages will give top evet occurrece probability ifluece this is the basic evet probability importace degree Usig the top evet occurrece probability fuctio is a liear fuctio of this ature idepedet evet probability importace degree coefficiet Qi of a partial derivative gives the basic Calculatio of fault tree evet occurrece probability The expert ivestigatio method is oe of the most commoly used methods to determie the probability of evet occurrece As the obect to obtai iformatio experts make udgmets assessmet ad predictio method relyig o their kowledge ad experiece Whe the expert use atural laguage such as wee small lesser medium biggish large prodigious to describe the basic probability as a result of these atural laguage with a certai ambiguity Basic probability ca ot use traditioal methods Therefore fuzzy set theory is employed to deal with these ucertai iformatio with the triagular fuzzy umber or trapezoid fuzzy umber replace the atural laguage the fuzzy umber expressio form as show i Figure 2 [ 7] Figure 2 Represets the atural laguage i the mathematical model For reciprocatig compressor system if the bottom evet probability of the" valve ed is determied by Fuzzy set ad Del Delphi method there are 4 maor steps: amely the selectio of experts make subective udgmets; expert atural laguage ito fuzzy umber; fuzzy umbers are trasformed ito fuzzy likelihood value; fuzzy probability value ito the fuzzy failure rate ca be estimated accordig to the followig steps ( expert to make subective udgmets choose 5 differet areas experts from valve desig costructio istallatio repair ad maagemet to form assessmet group ad udge the bottom evet probability o of valve ed or (2 Trasform the atural laguage ito fuzzy relatio Figure 2 is a atural laguage fuzzy umber forms its membership fuctio:
2652 Advaced Materials ad Process Techology f FL x 02 (02 x 03 (03 x 04 05 x (04 x 05 0 ( others (5 f L x ( x 02 03 x (02< x 03 0 ( others x 04 x 05 (05 x 06 (04 x 05 06 x (06 x 07 f M f (05 x 06 F H 08 x 0 (07 x 08 ( others (7 0 ( others (8 Formula: subscript FL L M FH are respectively o behalf of small small medium ad largethe [ 89] opiio of differet experts is combied with fuzzy sets ad the average algorithm The cut sets of type (5 to (8 respectively hypothesis: FL [ f f 2 ] L [ l ] l2 M [ m ] m2 FH [ h ] h2 f f 2 l l2 m m2 h h2 are the set upper ad lower limit of type (5 to (8 For f FL (x whe ( x 02 / f 02 f 2 05 0 ; similarly available: l l2 03 m 04 m2 06 0 h 05 h2 08 Expert group assessmet is small small medium large medium I the cut set expert group opiios of geeral fuzzy umber z: fhl M FLM HL max ffh fm ffl fm fl( x = 2 ( 04 ( 05 ( 02 ( 2(06 + ( 08 ( 05 (03 (9 Type (9 average fuzzy umber W: W (05 6(28 05 ( 032(056 (0 5 By fuzzy set extesio theory W is fuzzy sets To make W z z2 ( 032(056 so z 032 056 z2 or The average fuzzy umber W relatio fuctio is: x 032 (032 x 042 (042 x 046 f F H ( 056 x (046 x 056 0 ( others (3 Trasformer the fuzzy umbers ito fuzzy likelihood value The fuzzy probability value ( represets the expert o a give evet likelihood cofidece Based o the Cheg ad Hwag [7] proposed about fuzzy rakig method this paper trasforms the fuzzy umber ito The maximum fuzzy set ad the miimum fuzzy set is defied as: (6
Applied Mechaics ad Materials Vols 27-29 2653 x (0 x f max 0 ( others x (0 x (2 f max (3 0 ( others The possible values of Fuzzy umber fuzzy average: R ( W sup fw f max 0509(4 L ( W sup fw f mi 0 682 (5 x So W fuzzy likelihood value for: R ( W L ( W T ( W 0 4455 (6 2 (4 Trasform ambiguity may value ito the fuzzy real efficiecy ( FFR I order to esure the real efficiecy ad fuzzy efficiecy cosistecy betwee the fuzzy values must be trasformed ito fuzzy real efficiecy ( 0 k FRE 0 k ( / 3 230 (7 ( 0 0 3 fuzzy failure rate of Fuzzy umber W( FFR 334850 the probability of valve plate surface 3 debris is equal to 33485 0 Ad so o other bottom evet probability of reciprocatig compressor fault tree ca be calculatedcalculate top evet occurrece probability ad the bottom evet probability importace degree fid out the most importat ifluece factors of reciprocatig compressor failure provide guidace for reciprocatig compressor repair ad maagemetimprove its safety ad reliabilitythis shows that the mai factors of Reciprocatig compressor failure is the valve ad pressure packig rig fault;the secod is the pisto rig pisto ad pisto rod ad the cylider faultthe results ca be used for the maiteace ad improvemet of reciprocatig compressor desig theory Coclusio Based o the fuzzy fault tree the author uses the combiatio of fuzzy set theory ad expert udgmet method aalysis the Reciprocatig Compressors Fault Tree of evets ad the probability of top evet qualitatively ad quatitatively effectively overcome the traditioal fault tree aalysis errors from the failure probability of basic evet as a precise value improve the Reciprocatig Compressors Fault Diagosis techique Refereces [] Jilog Zhag The research ad Applicatio of Fuzzy diagosis method for reciprocatig compressor[d]dalia Uiversity of Techology2005 I Chiese [2] DighuaShi Sogrui Wag The fault tree aalysis method ad theory [M] Beiig Normal Uiversity press993 [3] Jidog Dig Yulig Ji Reciprocatig gas compressor commo faults ad troubleshootig [J ] Chia Equipmet Egieerig2004: 39-40 I Chiese [4] JiagZhu Quag zhi Lou A large reciprocatig compressor are examples of commo faults ad aalysis [J ] Compressor techology20046: 33-35 I Chiese [5]Juchao Wu The reciprocatig compressor fault aalysis [J] Chemical equipmet techology2007284: 65-67 [6] Shi Wag equivalet Fuzzy mathematics applicatio i artificial itelligece [M] Mechaical Idustry Press99 [7] Che Shu-Je H Wag Chi G-Lai Fuzzy multi2ple attribute decisio makig method sad applicatios[m] Berli :Spriger-Verlag 990 :250-252 [8 ] L IN CHIN-TORNG WANG MAO-J IUN J Hybrid fault tree aalysis usig fuzzy set s [J ] Reliability Egi2eerig ad System Safety 997 (58 :205-23 x
Advaced Materials ad Process Techology 04028/wwwscietificet/AMM27-29 The Study of Fault-Diagosis Method of Reciprocatig Compressor Based o Fuzzy Fault Tree Theory 04028/wwwscietificet/AMM27-292649